Loan Repayment Plan Comparison Calculator
Compare standard, graduated, and accelerated loan repayment plans to see total interest paid, monthly payments, and payoff timelines side by side.
Formulas Used
Standard Fixed Monthly Payment:
M = P × [r(1+r)n] / [(1+r)n − 1]
where P = principal, r = monthly interest rate (annual rate / 12), n = total months
Total Interest Paid:
Total Interest = (M × n) − P
Graduated Plan:
Initial payment P0 is solved numerically (bisection) so that the amortizing balance reaches zero at term end, with payments increasing by the specified percentage every 2 years.
Accelerated Plan:
Monthly payment = Standard M + Extra Payment. Balance is amortized month-by-month until fully paid. Payoff month is when balance ≤ $0.01.
Monthly Amortization Step:
Balancet+1 = Balancet × (1 + r) − Paymentt
Assumptions & References
- Interest compounds monthly (most common for personal, auto, and student loans).
- Graduated payments increase every 2 years, consistent with U.S. federal student loan graduated repayment structure (Federal Student Aid, studentaid.gov).
- Accelerated plan applies the extra payment entirely to principal reduction each month.
- No origination fees, prepayment penalties, or balloon payments are modeled.
- Standard amortization formula per Investopedia: Amortization Calculation Formula.
- All monetary values are in nominal (not inflation-adjusted) dollars.
- Graduated plan initial payment is solved via bisection to ensure the loan is fully repaid within the original term.